# At what speed does windchill give way to frictional heating?

29 May 2011

## Question

I recently started commuting by bicycle, but now that it's becoming winter, I've been wondering more about windchill. I understand much of it involves the moisture in the air, but how come commercial airplanes land from flights with cold icy surfaces, while some supersonic jets and reentering spacecraft land with a hot surface because of atmospheric friction?

At what point is the threshold? Is there a room temperature flight velocity?
And how fast will I need to ride my bike for atmospheric friction to overcome windchill and keep me warmer?

We put this question to Kevin Knowles from Cranfield University and Holger Babinski from Cambridge University...

Kevin - I'm Kevin Knowles. I'm professor of aeromechanical systems for Cranfield University and I work at the Defence Academy of UK in Shrivenham, Oxfordshire. In essence, the answer to the question is that aircraft wings are cold because they fly high in the atmosphere, the region known as the troposphere, and atmospheric temperatures fall with altitude in the lower atmosphere. So an aircraft flying at about 10 kilometres which is typical above the ground, a day where it's only 15 degrees Celsius at sea level, will be experiencing temperatures of about minus 50 Celsius outside.

If, however, you move fast enough in excess of the speed of sound then there's a significant kinetic heating effect and that's what spacecrafts experience. For example, if an aircraft were again flying at 10 kilometres altitude, but now at nearly at 7 times the speed of sound, then the temperature that it would feel due to kinetic heating, the highest temperature would be about 10 times the ambient temperature, but measured in degrees Kelvin.

Now, 10 kilometres altitude, the temperature in Kelvin is 223, so Mach 7 spacecrafts would experience 10 times that, so its heat temperature would be 2,200 Kelvin or about 2,000 degrees centigrade. At 10 kilometres, those two effects balance out if you're flying at about Mach 1.2, so at that speed, the kinetic heating is just enough to bring the peak skin temperature up to sea level temperature.

Diana - So it's not so much the wind-chill effect as the fact that planes fly around in the colder part of the atmosphere. Travelling at Mach 2, Concorde used to experience surface temperatures over 100 degrees Celsius causing the fuselage to extend by as much as a foot. But what if you're a cyclist?

Holger - Hello. My name is Holger Babinski and I'm professor of aerodynamics in the engineering department of Cambridge University. How much friction you need to compensate for the fact that the air is cold around you depends very much on the temperature difference between your body temperature and the air temperature.

You asked how fast you would have to cycle, so I shall assume that you're cycling at sea level. There, the surrounding temperature on a cold day might be something like 17 degrees. And in order to generate enough friction to bring the air up to body temperature, you have to cycle at about 63% of the speed of sound. With the speed of sound at sea level, that is pretty much 480 miles per hour. So you have to be pretty fast to achieve that.